Recursive multiplication


How can I get ASSY_EXT_QTY to be the quantity of all the path?
IE:

LVL   QTY   ASSY_EXT_QTY
1     1     1
2     3     3 1*3
3     2     6 1*3*2
...

I thought making a path but for the quantities and then somehow multiply them but this seems far reached. This is the code:

select
  LEVEL,
  SYS_CONNECT_BY_PATH(CHILD_ITEM_NUMBER, '>') ROUTE,
  CASE
    LEVEL
    WHEN 1 THEN COMPONENT_QTY
    ELSE (PRIOR COMPONENT_QTY) * COMPONENT_QTY <--- RIGHT NOW I'M DOING THIS BUT NOT ENOUGH AS WORKS IN THE CURRENT SUB-LEVEL ONLY.
  END ASSY_EXT_QTY
from
  (
    select
...
    FROM
...
    WHERE
...
  ) START WITH FATHER_ITEM_NUMBER = :ASSY CONNECT BY PRIOR CHILD_ITEM_ID = STR_ITEM_ID
) bom

Thanks!